Siegel Brownian motion
Probability
2023-09-11 v1
Abstract
We construct an analogue of Dyson Brownian motion in the Siegel half-space H that we term Siegel Brownian motion. Given \beta in (0,\infty], a stochastic flow for Z_t in H is introduced so that the law of the eigenvalues \lambda_t of the cross ratio matrix R(Z_t,iI_n) is determined by the Ito differential equation corresponds to stochastic gradient ascent of a function S. S turns out to be the log volume of isospectral orbit in H and can be understood as a Boltzmann entropy. In the limit \beta=\infty, the group orbits evolve by motion by minus a half times mean curvature.
Cite
@article{arxiv.2309.04299,
title = {Siegel Brownian motion},
author = {Govind Menon and Tianmin Yu},
journal= {arXiv preprint arXiv:2309.04299},
year = {2023}
}